Doping Profile in Planar Hybrid Perovskite Solar Cells Identifying

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Doping Profile in Planar Hybrid Perovskite Solar Cells Identifying Mobile Ions Mathias Fischer, Kristofer Tvingstedt, Andreas Baumann, and Vladimir Dyakonov ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.8b01119 • Publication Date (Web): 08 Oct 2018 Downloaded from http://pubs.acs.org on October 8, 2018

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ACS Applied Energy Materials

Doping Profile in Planar Hybrid Perovskite Solar Cells identifying Mobile Ions Mathias Fischer1, Kristofer Tvingstedt1, Andreas Baumann2*, and Vladimir Dyakonov1,2* 1

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Julius Maximilian University of Würzburg, 97074 Würzburg, Germany

Bavarian Center for Applied Energy Research, 97074 Würzburg, Germany

AUTHOR INFORMATION Corresponding Author *[email protected], [email protected]

ACS Paragon Plus Environment

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The role of ions in organo-metal halide perovskites and its impact on optoelectronic device performance remains one of the most intriguing issues in the field. The current-voltage hysteresis often observed in hybrid perovskite solar cells has been assigned to the presence of mobile ions inside the perovskite layer. The difficulty in studying electronic properties of solar cells results from the screening effects as well as slow dynamics of mobile ions particularly if they are located at the interfaces. In this work, we addressed the distribution of charged species in planar type methylammonium lead iodine (MAPI) as well as formamidinium lead iodine (FAPI) solar cells by using a modified capacitance-voltage (CV) method without illumination in combination with a Mott-Schottky (MS) analysis of experimental data. The characteristic Mott-Schottky behavior with a linear dependence of C-2(V), distinctive for a pn-junction, is not visible in pristine devices. Surprisingly, biasing the device in the forward direction results in MS behavior, which is due to the field-driven redistribution of mobile ions from the interface towards the absorber bulk. From the MS analysis, we deduced space charge concentrations of 2.5 x 1016 cm-3 and 2.8 x 1016 cm-3 for the FAPI and the MAPI device, respectively. However, the junction formation effect is not sustainable, since mobile ions relax to their initial location at ambient condition. But if the pre-biasing is done at temperatures slightly below room temperature, the pnjunction can be stabilized for the FAPI device. In contrast, the MAPI device shows a rapid redistribution of mobile ions back to the transport layers during the measurement even at lower temperatures. This can be observed in the quite different doping profiles for the two perovskite devices.


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KEYWORDS Perovskite solar cells, electrical impedance, Mott-Schottky analysis, ion migration, space charge region


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Organo-metal halide perovskites have risen to become one of the most studied thin film solar cell materials within the last decade. With an impressive increase in power conversion efficiency (PCE) from 3.8 % in 2008 to above 22 % in 2017, this kind of thin film PV technology has attracted the interest of the whole PV community. In order to design new solar cell architectures, a detailed knowledge about the material properties is required. Despite the well-known fact that doping of solar cells is a fundamentally important property, quite little attention has been spent on the doping concentration and distribution in perovskite solar cell. It has however been noted that the preparation methods may have an impact on the final doping distribution of the perovskite absorber [1]. Thus, very different interface physics is expected depending on whether the formation of the perovskite absorber takes place on top of a charge selective layer or vice versa, or whether the perovskite is formed via thermal evaporation or via solution processing. The formation of detrimental defects at the interface of the perovskite may not only reduce the solar cell parameters due to interfacial non-radiative recombination but also lead to the formation of charged defects such as iodine vacancies (VI) and iodine interstitials or methylammonium vacancies (VMA) [2, 3]. Especially the iodine vacancies and interstitials have been proposed to be mobile within the perovskite absorber due to a low activation energy and high diffusion rate [4]. While it is still under debate whether the hybrid perovskites should be considered as p- or n-type or even as an intrinsic semiconductor, the presence of mobile ions in the perovskite absorber is considered to affect the device performance strongly. In this matter, the almost omnipresent current-voltage hysteresis is assigned, at least partly, to the presence of mobile ions in the perovskite [5]. In general, mobile ions are among the most discussed issues in the field and they are frequently made responsible not only for current-voltage hysteresis, but also device degradation or inverted photocurrent transients which is assigned to be a direct evidence for field


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screening in the device [6-15]. The origin of ionic transport is still under debate and transport of iodine, methylammonium or even protons is proposed[2, 9, 16]. Such mobile ions will follow a diffusion potential gradient within the perovskite device. Hence, the ion distribution in hybrid perovskites can also be considered as a space charge distribution. When accumulating at the interface in the vicinity of the transport layer, this space charge will lead to a screening of the built-in potential which generally makes the interpretation of the capacitance-voltage behavior of solar cell devices extremely difficult [1]. A well-established experimental technique to study the space charge distributions in semiconductors, e.g. formed by a junction capacitance, is the Mott-Schottky (MS) analysis based on capacitance-voltage measurements (CV). The C(V) behavior can be understood by integrating the Poisson equation and treating the device as a plate capacitor. From the MS analysis, it is possible to determine directly the minority doping concentration ND as well as parameters such as the built-in potential Vbi according to =

(1)

With the elementary charge , the dielectric constant = and the vacuum permittivity. A prerequisite, however, is a clear identification of the C-2 Mott-Schottky region, i. e. the built-up of a depletion layer in the bulk or at the interface, which fulfills the Mott-Schottky equation [17]. In classical semiconductor devices with pn- or Schottky-junction, the capacitance-voltage dependence is typically governed by the formation of depletion (or space charge) layer between p- and n-doped regions of semiconductor and/or metal. The region, where no free charge carriers are present behaves as an insulator and is defined by the density of ionized dopants. This causes a certain capacitance which is in addition governed by the depletion layer width and the dielectric properties of the material according to Eq. 1. From the MS plot of the reciprocal square


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of capacitance versus voltage, the built-in potential can be determined by the linear extrapolation towards voltage axis from the intercept. This method, however, is restricted such that it can only be applied as long as no free electrons and/or holes are injected into the solar cell. Only in this case can the contribution of diffusion capacitance ∝ be neglected [16]. In perovskite solar cell devices, the applicability of MS analysis is challenging. With typical active layer thickness of around 300 - 500 nm and the fact that most of the perovskite semiconductors are believed to be rather intrinsic or at least not very heavily doped, the solar cell absorber layer is most likely fully depleted. The built-in potential in this case is then ruled by the work function difference of the contact materials. Another prerequisite for having a linear dependency in MS analysis is that the dopants (space charges) are homogeneously distributed in the bulk of the material [17, 18]. However, in case of the hybrid perovskite semiconductors it has to be considered that mobile ions are very likely to be present and possibly redistributed when an external voltage is applied on a time scale of several seconds, which will also lead to a change in the space charge distribution. Since it is unclear to what extent the redistribution of mobile ions can influence the overall charge carrier density in the active material, it is appropriate to differentiate between doping density, free charge carrier density and space charge density in this case as all space charges, including ions, must be considered in the Poisson equation which defines the built-in potential. In this work, the slow dynamics of charge redistribution in hybrid perovskites is used to the benefit to affect and probe the space charge profile formed at a particular voltage applied externally.


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Planar hybrid perovskite solar cells with two different perovskite absorbers namely methylammonium lead iodide (MAPI) and formamidinium lead iodide (FAPI) were fabricated. We used Poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine] (PTAA) as hole selective layer (HTL) and PCBM/C60 as electron selective layer (ETL) and bathocuproine (BCP) and gold (Au) as top contacts. Further details about the preparation of solar cells as well as their current-voltage characterization can be found in Supporting Information.

Figure 1: a) (left axes) and (right axes) of a FAPI and MAPI devices; b) Forward, reverse and reverse with pre-bias cycle of the FAPI device. The voltage used for pre-bias was 1.5 V applied for 20 s. We first conducted standard CV measurements by sweeping the voltage in forward direction from -0.4V to 1V while keeping the frequency constant at 10 kHz and the AC voltage amplitude to 20 mV. All capacitance measurements were done in Series-Mode. In this case, the resistor is in series with the plate capacitor. Further details on the CV measurements are provided in SI. In both types of devices, we observed a nearly voltage-independent capacitance in the range between -0.4 to 0.6 V, as can be seen in Figure 1a. This is consistent with the assumption of an


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intrinsic perovskite layer with the capacitance being essentially ruled by the thickness of the device which is then fully depleted. However, space charges at the contacts or transport layers as are often reported for hybrid perovskite solar cell devices [6] and assigned to charged defects such as iodine and methylammonium vacancies or interstitials would also lead to a capacitance which only slightly changes with voltage . In this case, the ions screen the external electric field hindering the latter to penetrate into the bulk of the perovskite. The range above 0.6 V is dominated by charge carrier injection, which means that Eq. (1) is no longer valid. As 1/C2 relation is not observed in the CV measurements shown in Figure 1, a direct employment of Eq. (1) would lead to non-realistic values of both or . To put in relation the validity of the Mott-Schottky analysis to doped semiconductors and to compare it to the here studied hybrid perovskites we performed CV scans on a standard silicon photodetector. The results are shown in SI (Fig. S4). Further, the capacitance remains voltage independent for both forward and backward sweeps with only a slight hysteresis being visible (see Figure 1b). However, the situation changes drastically when applying a forward voltage (further on called pre-bias) of more than 1 V for 20 s prior to the CV scan, followed by a 0.5 V/s fast CV scan in the reverse direction (from the pre-bias voltage to -0.4V). As can be seen in Figure 1b a MS-region begins to become visible which becomes more and more pronounced when the pre-bias voltage is further increased. We assign this phenomenon to the formation of two corresponding space charge layers within the perovskite absorber layer when applying the external electric field to the sample. Interestingly, in an immediate forward scan after pre-biasing, no MS behavior is visible and the CV diagram looks identical to a CV curve without pre-bias. This indicates that the formation of the space charge layers in the perovskite by the pre-biasing procedure is a slow process taking some time in the second range. And vice versa, the established space charge


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distribution is not very persistent relaxing to its initial value, as shown in the CV plot in the subsequent scan in forward direction. Taking the thermal dependence of ion motion into account, we lowered the sample temperature to 280 K and performed again the same set of experiments with the intention to prolong the persistency of the formed spaced charge region. We observed the same behavior as for 300 K, however, now with indeed a much more stable formation of the MS region during the time of CV measurement. We therefore assign the observed dynamic phenomenon to the presence of mobile ions. A schematic illustration is shown in Figure 2 which visualizes our hypothesis. A possible built-in potential created by the electron and hole transport material (ETM/HTM) will drive diffusion of mobile charges along the potential gradient, which also includes mobile ions. Under short circuit conditions, ions present in the perovskite absorber will move towards the respective transport layers. As the ETM (HTM) can be considered as nonconductive for ions an accumulation of the latter will occur at the interface to the respective transport materials, i. e. anions at the ETM and cations at the HTM (see Figure 2a). The accumulated ions will thus lead to the often-reported screening of the built-in potential [6,7].


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Figure 2 Schematic representation of the redistribution of mobile ions in the perovskite absorber, a) Ions at the interfaces does not allow the observation of a depletion layer capacitance, b) Forward bias redistributes mobile ions. c) When the bias is applied sufficiently long, a junction is created in the perovskite absorber, d) Depletion layer capacitance is measured with reverse voltage sweep. Low forward voltage only reduces the number of ions accumulated at the interface. If the forward voltage is high enough, a space-charge zone is built up over the bulk [19], showing a linear 1/C² - V behavior. When a bias is applied in forward direction, the ions are distributed within the perovskite, most importantly they are removed from the perovskite / transport layer interface. With respect to recent publications reporting defect migrations, iodine vacancies obey a relatively low activation energy of about 80 meV and are therefore considered to be very mobile. Moreover, the methylammonium vacancies VMA with a reported activation energy of 460 – 480 meV is another type of defects which is believed to be mobile even though on the time scale of milliseconds to seconds only [20, 21].. Depending on the magnitude of the applied pre-bias as well as its duration, the charged defects may be pushed from the respective interface into the bulk of the


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perovskite to form a junction capacitance inside the perovskite absorber, as in a typical pnjunction defined by a space charge concentration and a . Letter does imply a difference in the chemical potential between the n and p side of the junction originating from a local change in equilibrium charge carrier concentration. Thus, our findings can be understood as a bias induced self-doping effect of the perovskite absorber by ion redistribution. Consequently, by measuring the capacitance-voltage behavior under reverse bias, a voltage dependent depletion capacitance can be observed. We note that in such a generated pn-junction it is expected that positive and negative space charges are present in equal densities which requires a correction by a factor of 1/2 when determining the space charge density. After the pre-bias is removed from the device, the ions start to redistribute within the perovskite layer, until a state of equilibrium is reached, which corresponds to the initially accumulated charges at the edge of perovskite absorber. An important note here is that additional stationary dopants in the perovskite layer in the same or even greater amount than the mobile ions are unlikely, because the space charge layer would form at the interface and show MS behavior without applying pre-bias. Assuming a thermally activated motion of the ions in the perovskite, it is obvious that with decreasing the temperature the ion motion is lowered which will also lead to a slower redistribution of the ions after removal of the pre-bias voltage. In our case, already reducing the temperature by 20 K made it possible to measure the capacity of the depletion layer before the ions began to redistribute. In the following, we studied the junction capacitance in the FAPI as well as in a MAPI solar cell device by performing CV measurements at 280 K by applying a 2 V forward bias for different durations and then performing a 0.5 V/s fast CV sweep in reverse direction. In FAPI device, the MS-region at 280 K is much more pronounced compared to room temperature measurement, as shown Figure 3a. Carrying out fast CV scans every 10 s during pre-biasing, we


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were able to monitor the change in the space charge region in time. It is seen, that after 30 seconds of pre-biasing, a saturation is reached and the device in this state shows an almost ideal C-2-voltage dependence. According to Eq. (1) an average space charge concentration of 2.5 ± 0.1 ∗ 10() cm, and a built-in voltage of = 1.3 ± 0.1 V can be deduced for the FAPI device. This and space charge concentration is thus far more realistic than what is obtained for the device without the application of a pre-bias voltage, which may easily result in concentration in the order of 1018 to 1019 cm-3 when blindly fitting the slope of the capacitance drop. The concentration in the range of 1016 cm-3, however, fits well with values obtained for doped semiconductors as found also for the Si photodiode (see Figure S4). However, we note here that in silicon of course the dopants are most likely stationary and not mobile like in the mixed ionic-electronic perovskite semiconductors. In the case of the MAPI sample, the situation is however not so clear. After a pre-bias applied to the MAPI device for 60 s, a MS-region becomes visible in the CV sweep from positive to negative voltage. Interestingly, the C-2(V) dependence shows two linear regions with different slopes (see Fig. 3a). The almost constant capacitance in the voltage range from 0 V to 0.4 V is solely ruled by interfacial charges leading to values close to the purely geometric capacitance By fitting the two slopes, i. e. in the voltage range from 0.4 V to 0.6 V and from 0.6 V to 0.8 V it is obvious that only the slope in the latter voltage range results in meaningful parameters of = 1.0 ± 0.1 V and = 2.8 ± 0.1 ∗ 10() cm, . We assign the change of the C-2(V) dependence in the intermediate voltage range (0.4 V – 0.6 V) to the ion redistribution back to the contacts/transport layers which leads to the field screening effect. We want to note here that we cannot exclude that the fast redistribution of the ions already influences the slope in the MS region between 0.6 V and 0.8 V and hence the extracted Vbu and Nd. Thus, the values represent


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a lower estimate. Interestingly, this redistribution of ions in the MAPI happens on a faster time scale compared to the FAPI device. Assuming that the moving ions are iodine vacancies on the one hand and formamidinium (FA) and methylammonium (MA) ion vacancies on the other hand, we hypothesize that the positively charged FA vacancies move slower compared to the MA vacancies which is in agreement with the reported higher activation energy for migrating FA vacancies [22]. However, from the given set of data we cannot make a final conclusion here, and leave it open for future studies. Finally, the capacitance profile, i. e. the density of space charge as a function of the depletion width , can be determined from the CV measurements. The space charge concentration can be calculated from reciprocal voltage derivative of C-2(V) according to Eq. (1). Thereby, the change in capacitance is attributed to a change in the extent of the space charge region, using the relationship of a parallel plate capacitor =

/

0

, where A is device

active area and WD(V) is the voltage dependent depletion layer width. The value for was determined by measuring the capacitance of the fully depleted solar cell at 0.5 V reverse bias. The measured capacitance as a function of the frequency 1 is shown in figure S3. The constant plateau at this frequency for both devices present at 10 kHz can be assigned to the geometric capacitance due to dielectric relaxation of the bulk [1, 23-25], resulting in a relative dielectric constant of 24 for MAPI and 15 for FAPI. In Figure 3b, the capacitance profile is shown for both types of devices. For comparison the depletion width is normalized to the perovskite layer thickness which was measured to be 300 nm / 320 nm in case of the FAPI / MAPI device by using profilometer. The whitened part of the capacitance profiles in Figure 3b again correspond to charge carrier injection (see e.g. Figure 3a for V > 0.8V) which shrinks and finally diminishes the pn-junction


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in the bulk and thus represent a limitation in the resolution of the profile. For both devices, we found that charge carriers are initially located at the interface to the transport layers in which case the electric field is screened and thus ND is large at WD = 1 (WD equals sample thickness) dropping quickly for WD < 1 as can be seen in Figure 3b. When a pre-bias is applied to the device, mobile charges are pushed into the bulk of the perovskite which is visible in a decrease of ND at WD = 1 and a simultaneous increase of ND for WD < 1. With increasing duration of the pre-bias condition, the space charge concentration ND increases in the bulk and can be shrunk further by the CV scan until it reaches a saturation. For the FAPI device ND saturates at 2.5 x 1016 cm-3 at a depletion layer width of 68 % of perovskite layer thickness whereas in case of the MAPI a concentration of 2.8 x 1016 cm-3 at WD of around 55 % of perovskite layer thickness is reached. Comparing the shape of the two doping profiles, a clear difference can be observed. On the hand, the capacitance profile in the FAPI device shows an almost constant ion concentration of 2.5 x 1016 cm-3 for a wide range of varying depletion width from 70-90 % of the perovskite layer thickness indicating the rather stable formation of the junction capacitance in the FAPI device. For the MAPI device, however, a minimum in the profile can be observed from 60 % to 90 % of the perovskite layer thickness. This minimum corresponds to the slope in the MS plot in Figure 3a at lower voltages. As discussed above, only the slope at high voltages leads to meaningful parameters. Again, we assign the slope at lower voltages (V < 0.4 V) to a transition from the MS-region towards the almost voltage independent C-2 region which appears in the MAPI device already during the CV measurement. We associate this with a rapid redistribution of mobile ions back to their original position at the transport layer interface. To our knowledge, this is the first time that capacitance-voltage measurements have been used to identify mobile ion concentration in perovskite solar cell devices. In both MAPI and FAPI


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devices, we were able to determine ion concentration by means of MS analysis when a pre-bias was applied to the device prior to the CV scan, which pushes ions from the interface towards the bulk forming a pn-junction in the perovskite absorber. Concerning hybrid perovskites as mixed electronic-ionic conductors, the analysis of the ion concentration and its impact on the performance of optoelectronic devices in general becomes more and more relevant for a complete understanding and controlled improvement of those devices.

Figure 3 a) Mott-Schottky plots for the FAPI (circles) device when different pre-bias durations are applied. The depletion layer capacitance becomes visible when a forward bias is applied for


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more than 30 s; in case of MAPI (triangles) the change is less pronounced; (b) Capacitance profile of both devices. The minimum seen in the MAPI is assumed to be caused by ionic redistribution during the measurement. In conclusion, we studied two different hybrid perovskite planar p-i-n solar cells based on MAPI and FAPI as active layers. We performed CV measurements in order to determine the space charge carrier density by using the Mott-Schottky analysis. When applying a pre-bias to the solar cells up to 60 s and 2 V in forward direction we observed a hysteresis in the CV sweep indicating MS behavior (a linear C-2(V) dependence) in the first sweep from backward to forward direction which disappeared during the immediate forward sweep. However, when cooling down to 280 K, we find a more stable MS behavior in FAPI devices then in MAPI within the time of CV measurement. We attribute the appearance of the MS region to the mobile ions being initially located at the transport layer interface which are pushed into the bulk of the perovskite when a forward pre-bias is applied. Consequently, a pn-junction is formed in the perovskite absorber. For the unbiased devices the value for the interfacial charge concentration in the order of 10(2 cm, as well as their expansion is nominal in good agreement with findings from Belisle et al [6] out of photocurrent transients. The average concentration of the moving ion species is estimated to be in the range of 2.5 ∗ 10() cm, for FAPI and 2.8 ∗ 10() cm, for the MAPI device, which is in good agreement with values published by Cheng et al [15]. The almost equal densities hint towards a common origin of the moving ions, most probably iodide which is present in the same stoichiometric concentration for both materials. The resulting capacity profiles showed

that the space charge distribution reacts dynamically to the externally applied electric field. The work presented here gives a valuable insight into the properties of hybrid perovskite semiconductors for photovoltaic applications. With an established Mott-Schottky analysis, the


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space charge distribution in the semiconductor can provide important feedback to the device engineering when optimizing the individual layers and interfaces in the solar cell.

ASSOCIATED CONTENT Supporting Information AUTHOR INFORMATION Corresponding Author *Email: [email protected], [email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT The work was supported by the German Federal Ministry for Education and Research (BMBF) through the grant 03SF0514A/B (HYPER). K.T acknowledges the German Research Foundation (DFG) for funding through project 382633022 (RECOLPER). V.D. acknowledges the Bavarian State Ministry of Science and Arts for funding of the Collaborative Research Network “Solar Technologies go Hybrid”. A.B. works at the ZAE Bayern is supported by the Bavarian Ministry of Economic Affairs, Energy and Technology. We acknowledge Simon Berger for assistance in the preparation of perovskite solar cells.

REFERENCES


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Doping Profile in Planar Hybrid Perovskite Solar Cells Identifying

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